The area of a sector , with central angle 15° of a circle is 231cm² . if π = (22/7) , what is the the circumference(in cm) of the circle ?

central angle of a sector =  15°

The area of a sector = 231cm²

circumference(in cm) of the circle

we know that,

Area of sector with central angle as θ , and radius of circle as r is = (θ/360°) * π * (r)² .

given that,

Putting values we get,

→ (θ/360°) * π * (r)² = 231

→ (15°/360°) * (22/7) * r² = 231

→ (1/24) * (22/7) * r² = 231

→ 22 * r² = 231 * 7 * 24

dividing both sides by 2,

→ 11 * r² = 231 * 7 * 12

dividing both sides by 11,

→ r² = 21 * 7 * 12

→ r² = (7 * 7) * (3 * 3) * 4

→ r² = (7² * 3² * 2²)

→ r² = (7 * 3 * 2)²

→ r² = (42)²

square root both sides,

→ r = 42 cm.

Therefore ,

→ circumference of the circle = 2 * π * radius .

→ circumference of the circle = 2 * (22/7) * 42

→ circumference of the circle = 44 * 6

→ circumference of the circle = 264 cm .

Hence, circumference of the circle is 264 cm.

I hope it will help you.

Regards.

1 1/7 hope i

step-by-step explanation:

8/7 = (1 * 7 + 1) / 7 = 1 + 1/7 = 1 1/7